Finite Group Databasebeta

← #34069637

Subgroups — #34069637

Order 19328.

344 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 344 conjugacy classes of subgroups — too many to draw. Only its 89 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23752776C211yesmaximal, characteristic
2#23752218C212yesmaximal, complemented
3#23752186C211yesmaximal, characteristic, complemented
4#23751969C212yesmaximal, complemented
5#568×C151C211yesmaximal, characteristic, complemented
6C22×D604C2211yescharacteristic
7#18012735C412yescomplemented
8#18012728C412yescomplemented
9#18012713—22no—
10#18012707—22no—
11#18012698C2212yes—
12#18012698C2211yescharacteristic
13#18012661—24no—
14#18012654—22no—
15C2×#41×C151C2211yescharacteristic
16#131×C151—24no—
17C2×M16×C151—22no—
18C2×M16×C151C2212yes—
19C23×D151—21no—
20C2×D604—22no—
21C2×D604—21no—
22C2×D604—22no—
23C2×D604C2×C412yes—
24C2×C22⋊D151—24no—
25C4⋊Dic151—21no—
26C4⋊Dic151—22no—
27C22⋊Dic151—21no—
28C22⋊Dic151—22no—
29(C2×D151)⋊C4—24no—
30C4×Dic151—22no—
31C4×Dic151C2×C412yes—
32#41×C151—22no—
33#41×C151—22no—
34C2×Q8×C151C2×C411yescharacteristic
35C2×D4×C151C2×C411yescharacteristic
36C2×D4×C151D412yes—
37C22×C4×C151D412yes—
38C22×C4×C151C2311yescharacteristic
39M16×C151—24no—
40M16×C151—22no—
41M16×C151—22no—
42C2×C8×C151—24no—
43C2×C8×C151D414yescomplemented
44C22×D151—22no—
45C22×D151—42no—
46C22×D151—82no—
47D604—24no—
48D604—41no—
49D604—41no—
50C22⋊D151—84no—
51C2×Dic151—22no—
52C2×Dic151—42no—
53C23×C151C22⋊C412yes—
54C23×C151C2×D411yescharacteristic
55Q8×C151—22no—
56D4×C151—24no—
57D4×C151—22no—
58C2×C4×C151—22no—
59C2×C4×C151—22no—
60C2×C4×C151C22⋊C412yes—
61C2×C4×C151C22×C411yescharacteristic
62C2×C4×C151C2×D412yes—
63C2×C4×C151C2×D411yescharacteristic
64C2×C4×C151#4112yes—
65C8×C151—24no—
66C22×C151—22no—
67C22×C151—41no—
68C22×C151—42no—
69C22×C151C2×C22⋊C411yescharacteristic
70C22×C151#12112yes—
71C2×D151—44no—
72C2×D151—42no—
73C2×D151—84no—
74C4×C151—22no—
75C4×C151C4×D412yes—
76C4×C151#12011yescharacteristic
77C4×C151#12311yescharacteristic
78Dic151—42no—
79Dic151—82no—
80C2×C151—21no—
81C2×C151—22no—
82C2×C151—42no—
83C2×C151#38611yescharacteristic
84D151—82no—
85C151#191011yescharacteristic, complemented, Sylow
86#1910—1511nomaximal, Sylow
87#568D15111yescharacteristic, complemented
88#535—1511no—
89#418—1512no—
90#410—1511no—
91H(3,ℤ/4)—1512no—
92C2×#41C2×D15111yescharacteristic
93C22×D4—1511no—
94#131—24no—
95C2×M16—22no—
96C2×M16C2×D15112yes—
97#127—1512no—
98#124—1512no—
99#121—3022no—
100#120—3022no—
101#117—1512no—
102#117—1511no—
103#102—3024no—
104#99—3022no—
105C24—3021no—
106#41—22no—
107#41—22no—
108C2×Q8C4×D15111yescharacteristic
109C2×D4—3024no—
110C2×D4—3022no—
111C2×D4—3021no—
112C2×D4—3022no—
113C2×D4—1512no—
114C2×D4C4×D15111yescharacteristic
115C2×D4D60412yes—
116C22×C4C22⋊D15112yes—
117C22×C4C22×D15111yescharacteristic
118M16—24no—
119M16—22no—
120M16—22no—
121C2×C8—24no—
122C2×C8C22⋊D15114yescomplemented
123C4⋊C4—3021no—
124C4⋊C4—3022no—
125C22⋊C4—3021no—
126C22⋊C4—3024no—
127C22⋊C4—3022no—
128C42—3022no—
129C42—1512no—
130C23—3022no—
131C23—6042no—
132C23—12082no—
133C23(C2×D151)⋊C412yes—
134C23C2×D60411yescharacteristic
135Q8—22no—
136D4—24no—
137D4—22no—
138D4—3024no—
139D4—6041no—
140D4—6041no—
141D4—12084no—
142C2×C4—22no—
143C2×C4—22no—
144C2×C4—3022no—
145C2×C4—6042no—
146C2×C4(C2×D151)⋊C412yes—
147C2×C4C2×C4×D15111yescharacteristic
148C2×C4C2×C22⋊D15112yes—
149C2×C4C2×C22⋊D15111yescharacteristic
150C2×C4#1455900412yes—
151C8—24no—
152C22—22no—
153C22—41no—
154C22—42no—
155C22—6044no—
156C22—6042no—
157C22—12084no—
158C22C2×(C2×D151)⋊C411yescharacteristic
159C22#1801271312yes—
160C4—22no—
161C4—6042no—
162C4—12082no—
163C4C4×C22⋊D15112yes—
164C4#1801270811yescharacteristic
165C4#1801272211yescharacteristic
166C2—21no—
167C2—22no—
168C2—42no—
169C2—12082no—
170C2#2375209111yescharacteristic
subgroupG/H
centerC2#23752091
commutatorC2×C4×C151C22×C4
FrattiniC22×C4C22×D151
Fitting#568×C151C2
socleC2×C151#386
prime radical#23752776C2
cosocleC22×C4×C151C23
hypercenter#568D151
hypocenterC151#1910
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C2 ◁ C22×C4 ◁ #568

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #23752218C2semidirect
3. #23752186C2semidirect
4. #23751969C2semidirect
5. #568×C151C2semidirect
7. #18012735C4semidirect
8. #18012728C4semidirect
43. C2×C8×C151D4semidirect
85. C151#1910semidirect
87. #568D151semidirect
122. C2×C8C22⋊D151semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#237527762
#237522182
#237521862
#237519692
#568×C1512
#1910151